PLEASE Answer in details, Must Require Formulas

You have been working for a year as an analyst for an investment company that specializes in serving very wealthy clients. These clients often purchase shares in closely held investment funds with very limited numbers of stockholders. In fall of 2008, the market for certain types of securities based on real estate loans simply collapsed as the subprime mortgage scandal unfolded. Your firm, however, sees this market collapse as an opportunity to put together a fund that purchases some of these mortgage-backed securities, which investors have shunned, at bargain prices and holding them until the underlying mortgages are repaid or the market for these securities recovers.

The investment company has begun putting together sales information concerning the new fund and has made the following predictions regarding its possible performance over the coming year as function of how well the economy does:

State of the Economy Rapid expansion	Probability 10%	Fund Return 50%
Modest growth	50%	35%
No growth	40%	5%
Recession	5%	-100%

Your boss has asked you to perform a preliminary analysis of the new funds performance potential for the coming year. Specifically, he has asked you to address the following issues:

Required:

PLEASE Answer IN details ,include Formulas and show your steps.

A. What is the expected rate of return and standard deviation for the fund, given the estimates of fund performance in different states of the economy?

B. What is the reward-to-risk ratio for the fund based on the funds standard deviation as a measure of risk?

C. What is the expected rate of return for the fund based on the capital asset pricing model (CAPM)?

D. In addition to the information provided, you have observed that the risk-free rate of interest for the coming year is 4.5%, the market risk premium is 5.5%, and the beta for the new investment is 3.55. based on your analysis, do you think that the proposed fund offers a fair return, given its risk? Explain.